• Question: Where does the energy for electron degeneracy come from in the cores of white dwarf stars?

    Asked by idontknoww to Amy, Grant, Martin, Shawn, Usman on 18 Mar 2013.
    • Photo: Martin Archer

      Martin Archer answered on 18 Mar 2013:

      So when people talk about electron degeneracy in stars, it’s down to a fundamental property of matter – the Pauli exclusion principle. This says that you can’t have 2 things in exactly the same state. The implications of this are that not all particles can be in the lowest energy level possible because they get filled up first. That means that more and more particles have to be other energy levels. So no matter how hard you try you can’t force matter to a lower energy state. In stars this is like a pressure preventing the star from being compressed any further.

    • Photo: Amy Tyndall

      Amy Tyndall answered on 19 Mar 2013:

      To add to what Martin wrote:

      The resulting pressure generated by this electron degeneracy will stop a white dwarf from collapsing in on itself, if its mass is below 1.44-times the mass of our Sun (the ‘Chandrasekhar limit’). If the white dwarf is larger than 1.44 solar masses, it will continue to collapse as the degeneracy pressure will be a lot weaker than the crushing force of gravity, and gravity will ‘win’.

      It will then go on to form a neutron star (if the mass is between 1.44 and 3 solar masses), or a black hole (if the mass is greater than 3 solar masses).

      Interesting facts! :
      1 teaspoon of white dwarf = 5 tonnes
      1 teaspoon of neutron star = 6 billion tonnes
      1 teaspoon of black hole = 2 x the mass of the Earth! (if a black hole were actually a solid object)

    • Photo: Grant Kennedy

      Grant Kennedy answered on 21 Mar 2013:

      That’s a really tough question, and as Martin said the answer lies with the details of quantum mechanics.

      What the Pauli exclusion principle means is that you can’t compress the White dwarf so much that the electrons all have the same state. It’s the same reason that electrons in an atom have to have different energy levels (called “orbitals”) and they can’t all sit at the lowest energy level. It’s not that energy is needed to keep them up at higher levels, it’s that they can’t actually all get to the lowest level, and if you try to push them, they push back!

      The same thing is going on in a White dwarf, the gravity from the star is trying to squash everything down, but the electrons can’t all go into the lowest energy level, so they resist being squashed. This resistance is a pressure, because is pushes back against the gravity.

      The degeneracy pressure can be beaten if you squash hard enough though, so if you add enough mass to a White dwarf eventually gravity wins. Then the electrons combine with protons to form neutrons, and everything squashes down even further. However, there’s also a degeneracy pressure for neutrons, so what you get is a neutron star that is supported by neutron degeneracy pressure.

      This degeneracy pressure can also be beaten, but now we’re getting beyond our knowledge of how things actually behave at such crazy densities, and what happens is a bit uncertain. One possibility is that is turns into a black hole!

      g

Comments

  • Photo: idontknoww

    idontknoww commented on :

    That’s not true, in stars larger then 1.4 solar masses the gravity pull the electrons into protons and causes anti-beta decay, what I want to know is where is the energy coming from for this electron to be moving so rapidly.

  • Photo: Martin

    Martin commented on :

    It is true, but what you’re asking now is a slightly different question! As you say, it’s gravity which is pulling the star together making it a lot denser and because it’s so dense the likelihood of electrons merging with protons is much greater. So in effect its gravitational potential energy that’s being converted into kinetic energy which then gets turned into mass (neutrons are slightly heavier than protons).